Question

An investor is forming a portfolio by investing $150,000 in stock A which has a beta of 2.40, and $150,000 in stock B which has a beta of 0.60. The market risk premium is equal to 5% and treasure bonds have a yield of 3% (r_RF). What’s the portfolio beta?

		1.60
		1.95
		1.50
		1.80

Using the information in Question, calculate the required rate of return on the investor’s portfolio

		8.5%
		10.5%
		12.75%
		9.5%

Answer 1

Solution:

Calculation of Portfolio Beta :

The formula for calculating the Portfolio Beta is

β_P = [ ( W_A * β_A ) + ( W_B * β_B ) ]

where

β_P = Portfolio Beta

W_A = Weight of Investment in Stock A ;     W_B = Weight of Investment in Stock B ;   

β_A = Beta of Stock A    ;     β_B = Beta of Stock B ;

As per the information given in the question we have

Investment in Stock A = $ 150,000   ; Investment in Stock B = $ 150,000 ;

Total Investment in stocks = Investment in Stock A + Investment in Stock B

= $ 150,000 + $ 150,000 = $ 300,000

Thus,

W_A = Weight of Investment in Stock A = Investment in Stock A / Total Investment in stocks

= $ 150,000 / $ 300,000 = 0.50

Thus W_A = 0.50

W_B = Weight of Investment in Stock B = Investment in Stock B / Total Investment in stocks

= $ 150,000 / $ 300,000 = 0.50 ;    

Thus W_B = 0.50

β_A = Beta of Stock A = 2.40    ; β_B = Beta of Stock B = 0.60    ;

Applying the above vales in the formula we have portfolio beta as

= ( 0.50 * 2.40 )   + ( 0.50 * 0.60 )

= 1.20 + 0.30

= 1.50

Thus the Portfolio’s Beta is = 1.50

The solution is Option 3 = 1.50

Calculation of required rate of return on the investor’s portfolio:

Cost of required rate of return on the investor’s portfolio is calculated using the following formula :

R_E = r_RF + [ β * ( R_M - r_RF ) ]

Where

R_E = Required rate of return   ; r_RF = Risk free rate of return   ; β = Beta of the portfolio ;

( R_M – R_F ) = Market risk Premium ;

As per the information given in the question we have

R_F = Yield on treasure bonds = 3 %   ; ( R_M - R_F ) = Market Risk Premium = 5 %   ; β = 1.5

Applying the above values in the formula we have

= 3 % + ( 1.5 * 5 % )

= 3 % + 7.5 % = 10.5 %

Thus the Required rate of return = 10.5 %         

The solution is Option 2 = 10.5 %